In any gravitational stellar system, a combination of several
elements are responsible for the intricate (complex) mechanism of
the system (i.e., anisotropic stresses, dissipative variables,
irregular the behavior of energy density, etc.). In general, a
gravitational system having regular (in terms of energy density) and
isotropic (in terms of pressure) distribution is considered to have
minimal complexity. The dynamical gravitational structures have a
quite different interpretation of complexity, as compared to the
static structures [1]}, [2]}. In
this case, the \(f(\mathcal {G}, \mathbf {T}^{2})\)  corrections,
anisotropic stresses, structural variables, and irregular energy
density are the key ingredients to complex the gravitational system.
The dynamical variable \(Y_{TF}\)  constitutes a particular amalgam of
the above-stated parameters, as indicated in Eq.(REF ), and
therefore it is adopted as the \(\mathbb {C}_{\mathbf {F}}\)  for our
system. Later on, we will present several analytical solutions under
the condition \(Y_{TF}=0\) .
